User blog:Dimensional consciousness/4-fold symmetry sacred geometry and more
The E8 lie group as shown is the 231 gates+The flower of life+Metatrons cube(64 tetrahedron grid) and the flower of life that encodes the 64 tetrahedron grid/metatrons cube has 24 circles that surround its outside and these 24 circles produce the Prime Numbers Cross which is a 4-fold Symmetry, The Kathara grids sacred geometry is based around the number 4 and is based around a doubling sequence which can be produced the kathara grid doubling and encasing the lower one and this produces a spiral that looks just like the Fibonacci spiral which also produces a doubling sequence when it is used to form a triangle and i overlayed the Fibonacci spiral over the kathara grid which is interesting because the spiral produced by the kathara grid follows the same pathway the Fibonacci spiral does! 4-fold symmetry Fruit of life In this essay I'm going to propose two possible three-dimensional structures of the Fruit of Life. Each one is supported on a particular 3D inner grid that is contained into the inner grid of Metatron's Cube. This was a necessary condition for me, as the Fruit of Life is contained into the Flower of Life and the latter defines the Cube. Remember that in 2D the Fruit of Life is constructed after completing two outer layers of circles in the Flower of Life until obtaining three lines of five nonintersecting circles. First 3D structure: a cube of 3x3x3 spheres The two 3D structures that I propose require the completion of the remaining six circles in the 2D representation of the Fruit of Life. At first sight, the projection can be extended to three dimensions as a cube of 3x3 spheres per side, totaling 27 spheres The final result would be similar to Metatron's cube, but with a sphere less per edge. This geometry also matches the 26 pointed star discussed in Construction of sacred geometry using Pascals triangle through quantum atom theory and Kabbalah. This structure of spheres is clearly contained in Metatron's Cube. Coming from the 3D structure of the Egg of Life as a cube made of 2x2x2 spheres, the next step in a fractal growth would be the Fruit of Life as a cube made of 3x3x3 spheres, and the final step a cube made of 4x4x4 spheres that I claim to be Metatron's Cube. This process can be illustrated using the same XY projection of the grid coordinates from Metatron's Cube. The inner structue that supports the cube made of 3x3x3 spheres is not evident. You can obtain it by retaining any corner of size 3x3 from the inner grid of Metatron's Cube. The final result is the grid shown. You can see in that this grid has a big tetrahedron intersecting a set of four cuboctahedrons (actually vector equilibrium structures). These are distributed as one line made of two cuboctahedrons side by side, on top of another identical line rotated 90 degrees. The 27 spheres that form the 3D structure of the Fruit of Life can be tought of the 26 facets of a cube, plus a central sphere: the 6 faces are represented by the 6 central spheres in each side; the 8 vertices would be the 8 corner spheres; and the 12 edges are the remaining 12 outer spheres joining each couple of vertices. This cube made of 3x3x3=27 spheres admits an interpretation in terms of the trigrams. The trigrams are groups of three elements taken from three possible base essences: the Tao (a dot), the Yin (a line) and the Yang (a dotted line). This makes a total of 27 possible combinations. The trigrams can be assigned to these 26+1 facets of the cube in the form proposed by James Barton. The central sphere would correspond to the Tao; the spheres in the faces, to the 6 trigrams with two Tao elements; the spheres in the edges to the 12 trigrams with one Tao element; and the corner spheres to the 8 trigrams with only Yin and Yang. It is worth noting at this point that the set of 27 trigrams can be linked to the set of 64 hexagrams, which in turn coincide with the number of spheres in Metatron's Cube. Second 3D structure: a cuboctahedron of 55 spheres The augmented 2D Fruit of Life can also be thought as the projection of a three dimensional set of spheres distributed as a cuboctahedron instead of a cube. It is the big cuboctahedron contained inside the grid of Metatron's Cube. In this case, the spheres would occupy the vertices of the grid, instead of being located at the center of the small tetrahedrons defined by the grid (that's why we draw them in red instead of green). This grid can be seen as grown out from the central cuboctahedron (actually vector equilibrium) by a process of doubling the edge size. It is a fractal growth also in another sense: the central cuboctahedron contains 13 vertices, whereas the big cuboctahedron contains 13 smaller cuboctahedrons. Octahedron The first hexagon in the pattern of the Seed of Life (the first seven spheres in the construction of the Flower of Life) could be seen as the projection of an octahedron. That made me think that the star tetrahedron, which is the stellation of the octahedron, could also be a building block of Metatron's Cube. In fact, the star tetrahedron is very important at many scales: it is the blueprint of our light body, the Mer Ka Ba, but is has also been recognised in the inner energetic structure of planets and stars. The following is a representation of an orthogonal projection of the octahedron (left) and the star tetrahedron (right) on the X-Y plane (seen from the top in the preceding figure). If the inner square lies in this plane (z=0) and the edge length is 1, then the upper and lower central vertices of the octahedron, and the outer vertices of the stellated octahedron have height z=1/2. Lying strictly on the XY plane, the outer square of the projection of the star tetrahedron seems to have grown out by a factor2from the central square which represents the octahedron. This process can be further iterated a couple of times until we reach a size that can contain four star tetrahedrons. The side of the final square is twice the side of the original one. The inner grid of Metatron's Cube The preceding growth pattern can be extrapolated to three dimensions. Let's put two star tetrahedrons side by side. You will notice that there is (half) a central star tetrahedron. So we see that a central star tetrahedron can be surrounded by four more star tetrahedrons, and each of them shares with it two tetrahedrons. Now the question is: how can this structure grow to become the three dimensional grid of Metatron's Cube? Our preferred alternative (there is another alternative that we'll discuss at the end of this article) is to stack a layer of four star tetrahedrons onto the preceding one. I have come to the conclusion that this is the inner structure, the support grid of Metatron's Cube. We will see later that this structure contains other solids apart from its "biulding blocks", star tetrahedrons. You can observe that this grid is symmetric: what you see from above is the same as you would see from any of the four sides and from below. The following figure shows an XY projection of the grid from which you can extract the coordinates of each vertex. The central octahedron in each star tetrahedron is shown in grey. Source sacred-geometry.es Category:Blog posts